The story
Ultimately from Middle Persian mzdk, of uncertain pronunciation (and thus of uncertain etymology). Arabic reports and translations (9th-century onwards, e.g. al-Muqaffa) have mazdak. Sources in New Persian first appear two centuries later, and have mizdak, muzdak in addition to mazdak. Conventional European language spelling is informed by Theodor Nöldeke's late 19th-century studies of the primary sources.
Etymology from Wiktionary, CC BY-SA 4.0.